Vestrini was a cleric regular of the religious order of the Scolopi or Piarists, whose main aim was teaching and educating the youth.
From the title pages of his publications, we can deduce that Vestrini was a professor of moral philosophy and theology at the Cortona seminary, in the Grand Duchy of Tuscany, before becoming a lecturer in theology at the Collegio Nazareno in Rome.
Vestrini also gave lectures at the Accademia Etrusca in Cortona, of which he was a distinguished member. In 1753 he was elected as part of the committee aimed to reform the rules of the Accademia, and contributed to writing the Obblighi degli Accademici (1754).
In 1754, Vestrini was asked to write the sepulchral elegy for the bishop of Cortona Luigi Gherardi.